Performance analysis of distributed space-time block coding schemes in Middleton Class A noise

A performance analysis of distributed space-time block coding (STBC) schemes involving multiple decode-and-forward relays is carried out in the case of Middleton Class A impulsive noise, which is one of the major sources of performance degradation in many wireless systems. The considered cooperative communication framework, according to which the signal transmitted by each relay is the product of a STBC matrix and a proper vector of length $L$, encompasses both centralized and decentralized protocols. Since an insightful theoretical analysis of the maximum-likelihood (ML) detector is very challenging in non-Gaussian environments, an ideal version of the ML detector, which is referred to as ideal ML (IML), is considered, along with the suboptimal minimum distance (MD) detector. It is analytically proven that, with respect to Gaussian noise, the presence of impulsive noise does not affect the performance of both the IML and MD detectors in terms of {\em asymptotic} (i.e., when the transmit power is infinitely large) diversity order $R_{\text{max}}$, which is equal to the minimum between $L$ and the maximum number of cooperating nodes (relays plus source); in the case of the IML detector, the coding gain is unaffected, too. Closed-form formulas involving the main parameters of noise and STBC highlight that the major effect of the impulse noise on the performance of the IML and MD detectors concerns the {\em finite} signal-to-noise ratio (SNR) diversity order, which does not monotonously increase as the SNR rises; in the case of the MD detector, the coding gain is also affected by the impulsiveness of the noise. In particular, it is shown that, in the case of complex orthogonal STBC, the adverse effect of impulse noise on the performance of the IML detector tends to completely disappear for sufficiently large values of $R_{\text{max}}$, whereas increasing values of $R_{\text{max}}$ emphasize the weakness of the MD detector against non-Gaussian noise. Finally, simulation results are provided for the ML, IML, and MD detectors to corroborate and supplement the results derived theoretically.